RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2015-10-01_20:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.81 21.2572 0.785004 2 to 25 15.93 13.5613 0.302125 3 to 26 15.46 24.8110 0.900980 4 to 27 15.66 24.8041 0.900818 5 to 28 15.75 15.9706 0.474082 6 to 29 15.72 16.4763 0.509643 7 to 30 16.18 15.9866 0.475218 8 to 31 16.02 17.1670 0.556893 9 to 32 15.75 19.8110 0.715991 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.245431 Tough bday spacings test for dh-ranFile-2015-10-01_20:31: 4096 birthdays, year=2^32 days Table of Expected vs. Observed counts: Duplicates 0 1 2 3 4 5 6 7 8 9 >=10 Expected 9.2 36.6 73.3 97.7 97.7 78.1 52.1 29.8 14.9 6.6 4.1 Observed 7 35 79 105 91 86 47 20 18 7 5 (O-E)^2/E 0.5 0.1 0.4 0.5 0.5 0.8 0.5 3.2 0.7 0.0 0.2 Birthday Spacings: Sum(O-E)^2/E= 7.419, p= 0.315 RESULTS OF GCD FOR dh-ranFile-2015-10-01_20:31 Euclid's algorithm: p-value, steps to gcd: 0.266380 p-value, dist. of gcd's: 0.671278 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2015-10-01_20:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.495 0.159 0.375 0.276 0.152 0.962 0.946 0.180 Bits 8 to 15---> 0.672 0.142 0.725 0.871 0.008 0.881 0.351 0.148 Bits 16 to 23---> 0.063 0.209 0.717 0.431 0.853 0.613 0.220 0.249 Bits 24 to 31---> 0.623 0.183 0.678 0.072 0.312 0.271 0.363 0.658 KS test for the above 32 p values: 0.730 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2015-10-01_20:31, p-values for 5 runs: 0.5198, 0.0909, 0.6269, 0.6249, 0.3789 Rank test for binary matrices (31x31) for dh-ranFile-2015-10-01_20:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 216 211.4 0.099 0.099 r= 29 5092 5134.0 0.344 0.443 r= 30 23213 23103.0 0.523 0.966 r= 31 11479 11551.5 0.455 1.422 chi-square = 1.422 with df = 3; p-value = 0.300 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2015-10-01_20:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 196 211.4 1.124 1.124 r= 30 5194 5134.0 0.701 1.825 r= 31 22947 23103.0 1.054 2.879 r= 32 11663 11551.5 1.076 3.955 chi-square = 3.955 with df = 3; p-value = 0.734 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2015-10-01_20:31 b-rank test for bits 1 to 8, p=0.42707 b-rank test for bits 2 to 9, p=0.99440 b-rank test for bits 3 to 10, p=0.97871 b-rank test for bits 4 to 11, p=0.10658 b-rank test for bits 5 to 12, p=0.68977 b-rank test for bits 6 to 13, p=0.16067 b-rank test for bits 7 to 14, p=0.52125 b-rank test for bits 8 to 15, p=0.59666 b-rank test for bits 9 to 16, p=0.50717 b-rank test for bits 10 to 17, p=0.39592 b-rank test for bits 11 to 18, p=0.54225 b-rank test for bits 12 to 19, p=0.49516 b-rank test for bits 13 to 20, p=0.01517 b-rank test for bits 14 to 21, p=0.90464 b-rank test for bits 15 to 22, p=0.12990 b-rank test for bits 16 to 23, p=0.04472 b-rank test for bits 17 to 24, p=0.87720 b-rank test for bits 18 to 25, p=0.13408 b-rank test for bits 19 to 26, p=0.33195 b-rank test for bits 20 to 27, p=0.02163 b-rank test for bits 21 to 28, p=0.02428 b-rank test for bits 22 to 29, p=0.98713 b-rank test for bits 23 to 30, p=0.20857 b-rank test for bits 24 to 31, p=0.60598 b-rank test for bits 25 to 32, p=0.21802 TEST SUMMARY, 25 tests, each on 100,000 random 6x8 matrices The above should be 25 uniform [0,1] random variables: The KS test for those 25 supposed UNI's yields p = 0.150912 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2015-10-01_20:31 (20 bits/word, 2097152 words 20 bitstreams. No. missing words should average 141909.33 with sigma=428.00.) ---------------------------------------------------------------- BITSTREAM test results. Bitstream No. missing words z-score p-value 1 142406 1.16 0.877066 2 141101 -1.89 0.029471 3 141750 -0.37 0.354847 4 142347 1.02 0.846750 5 141412 -1.16 0.122621 6 142053 0.34 0.631443 7 142267 0.84 0.798332 8 142009 0.23 0.592070 9 142018 0.25 0.600214 10 142161 0.59 0.721739 11 142329 0.98 0.836590 12 141874 -0.08 0.467106 13 141800 -0.26 0.399190 14 142674 1.79 0.963000 15 141986 0.18 0.571084 16 142818 2.12 0.983126 17 141863 -0.11 0.456900 18 141689 -0.51 0.303350 19 142407 1.16 0.877541 20 142695 1.84 0.966797 ---------------------------------------------------------------- OPSO test for dh-ranFile-2015-10-01_20:31 Bits used No. missing words z-score p-value 23 to 32 141933 0.0816 0.532526 22 to 31 142531 2.1437 0.983971 21 to 30 141887 -0.0770 0.469312 20 to 29 142141 0.7989 0.787815 19 to 28 142260 1.2092 0.886708 18 to 27 141754 -0.5356 0.296110 17 to 26 142271 1.2471 0.893827 16 to 25 141558 -1.2115 0.112855 15 to 24 141763 -0.5046 0.306925 14 to 23 141957 0.1644 0.565284 13 to 22 142408 1.7196 0.957243 12 to 21 141517 -1.3529 0.088050 11 to 20 141852 -0.1977 0.421644 10 to 19 142002 0.3196 0.625346 9 to 18 142299 1.3437 0.910476 8 to 17 142224 1.0851 0.861054 7 to 16 142112 0.6989 0.757681 6 to 15 142265 1.2264 0.889985 5 to 14 142229 1.1023 0.864837 4 to 13 142186 0.9540 0.829967 3 to 12 142003 0.3230 0.626652 2 to 11 142100 0.6575 0.744565 1 to 10 142129 0.7575 0.775620 ----------------------------------------------------------------- OQSO test for dh-ranFile-2015-10-01_20:31 Bits used No. missing words z-score p-value 28 to 32 141790 -0.4045 0.342919 27 to 31 142094 0.6260 0.734343 26 to 30 142429 1.7616 0.960931 25 to 29 141686 -0.7571 0.224510 24 to 28 141918 0.0294 0.511723 23 to 27 142229 1.0836 0.860735 22 to 26 141752 -0.5333 0.296905 21 to 25 142483 1.9446 0.974091 20 to 24 141599 -1.0520 0.146408 19 to 23 142054 0.4904 0.688077 18 to 22 141987 0.2633 0.603836 17 to 21 141944 0.1175 0.546778 16 to 20 141378 -1.8011 0.035842 15 to 19 141748 -0.5469 0.292230 14 to 18 141676 -0.7909 0.214487 13 to 17 142243 1.1311 0.870990 12 to 16 142457 1.8565 0.968309 11 to 15 142241 1.1243 0.869558 10 to 14 141615 -0.9977 0.159205 9 to 13 141661 -0.8418 0.199951 8 to 12 141622 -0.9740 0.165028 7 to 11 142117 0.7040 0.759273 6 to 10 142083 0.5887 0.721973 5 to 9 141853 -0.1909 0.424283 4 to 8 141964 0.1853 0.573512 3 to 7 142118 0.7074 0.760327 2 to 6 142556 2.1921 0.985814 1 to 5 141886 -0.0791 0.468483 ----------------------------------------------------------------- DNA test for dh-ranFile-2015-10-01_20:31 Bits used No. missing words z-score p-value 31 to 32 141828 -0.2399 0.405199 30 to 31 141708 -0.5939 0.276292 29 to 30 142025 0.3412 0.633527 28 to 29 142721 2.3943 0.991674 27 to 28 142531 1.8338 0.966661 26 to 27 142523 1.8102 0.964870 25 to 26 142127 0.6421 0.739594 24 to 25 142178 0.7925 0.785976 23 to 24 142205 0.8722 0.808446 22 to 23 141999 0.2645 0.604308 21 to 22 142009 0.2940 0.615626 20 to 21 141865 -0.1308 0.447980 19 to 20 142812 2.6627 0.996125 18 to 19 142462 1.6303 0.948480 17 to 18 141935 0.0757 0.530180 16 to 17 142033 0.3648 0.642373 15 to 16 141322 -1.7325 0.041589 14 to 15 141249 -1.9479 0.025715 13 to 14 142103 0.5713 0.716101 12 to 13 141661 -0.7325 0.231921 11 to 12 141720 -0.5585 0.288253 10 to 11 141884 -0.0747 0.470219 9 to 10 142633 2.1347 0.983608 8 to 9 142215 0.9017 0.816387 7 to 8 141913 0.0108 0.504319 6 to 7 141644 -0.7827 0.216906 5 to 6 141578 -0.9774 0.164192 4 to 5 141570 -1.0010 0.158420 3 to 4 141897 -0.0364 0.485493 2 to 3 141311 -1.7650 0.038783 1 to 2 141138 -2.2753 0.011444 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2015-10-01_20:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2509.95 0.141 0.555944 Test results for specific bytes for dh-ranFile-2015-10-01_20:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2687.94 2.658 0.996068 2 to 9 2558.58 0.828 0.796287 3 to 10 2567.71 0.958 0.830870 4 to 11 2510.88 0.154 0.561146 5 to 12 2546.25 0.654 0.743458 6 to 13 2497.87 -0.030 0.487981 7 to 14 2549.39 0.698 0.757547 8 to 15 2520.47 0.289 0.613877 9 to 16 2376.97 -1.740 0.040944 10 to 17 2513.17 0.186 0.573891 11 to 18 2533.33 0.471 0.681321 12 to 19 2435.86 -0.907 0.182190 13 to 20 2587.80 1.242 0.892812 14 to 21 2421.67 -1.108 0.133980 15 to 22 2452.60 -0.670 0.251325 16 to 23 2521.01 0.297 0.616788 17 to 24 2395.65 -1.476 0.070014 18 to 25 2512.49 0.177 0.570084 19 to 26 2568.79 0.973 0.834696 20 to 27 2501.75 0.025 0.509882 21 to 28 2634.87 1.907 0.971762 22 to 29 2514.87 0.210 0.583306 23 to 30 2496.72 -0.046 0.481516 24 to 31 2340.13 -2.261 0.011881 25 to 32 2458.41 -0.588 0.278187 CDPARK for dh-ranFile-2015-10-01_20:31: result of 10 tests (Of 12000 tries, the average no. of successes should be 3523.0 with sigma=21.9) No. succeses z-score p-value 3489 -1.5525 0.060270 3492 -1.4155 0.078457 3546 1.0502 0.853193 3554 1.4155 0.921543 3561 1.7352 0.958644 3543 0.9132 0.819442 3525 0.0913 0.536383 3542 0.8676 0.807188 3492 -1.4155 0.078457 3540 0.7763 0.781201 Square side=100, avg. no. parked=3528.40 sample std.=26.03 p-value of the KSTEST for those 10 p-values: 0.135259 Results for the MINIMUM DISTANCE test for dh-ranFile-2015-10-01_20:31 0.8968,0.2950,0.6329,0.2812,0.7235,0.7659,0.0569,0.1992,0.4340,0.2076, The KS test for those 10 p-values: 0.874970 The 3DSPHERES test for dh-ranFile-2015-10-01_20:31 sample no r^3 equiv. uni. 1 27.186 0.595940 2 14.067 0.374315 3 18.606 0.462165 4 20.353 0.492594 5 120.145 0.981772 6 39.551 0.732428 7 8.702 0.251794 8 13.506 0.362496 9 50.629 0.815041 10 2.368 0.075914 11 12.134 0.332659 12 31.325 0.648020 13 192.814 0.998383 14 113.171 0.977003 15 18.951 0.468311 16 16.950 0.431635 17 40.011 0.736499 18 23.051 0.536225 19 8.730 0.252493 20 32.308 0.659358 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.272854 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2015-10-01_20:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) 1.3 -0.3 0.8 0.0 0.5 0.2 0.7 1.2 -0.7 -0.3 0.9 1.6 0.7 -0.0 -1.2 -0.1 0.4 -0.2 1.1 -0.8 1.1 -0.9 0.2 -1.5 -0.2 -1.3 -0.7 -1.2 -0.7 0.3 0.9 0.0 -0.2 2.3 -0.1 0.1 -0.2 0.8 2.1 0.4 0.1 -1.0 -0.1 Chi-square with 42 degrees of freedom:33.777090 z-score=-0.897193, p-value=0.186888 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2015-10-01_20:31 Test no p-value 1 0.494402 2 0.025640 3 0.723222 4 0.223289 5 0.040084 6 0.088065 7 0.075071 8 0.015064 9 0.025619 10 0.013665 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.000017 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2015-10-01_20:31: (for k>=2, the prob. of a run of length k is 2*k/(k+1)!) Length Expected UpRuns (O-E)^2/E DownRuns (O-E)^2/E 2 66666.67 66682 0.00 66568 0.15 3 25000.00 24960 0.06 25001 0.00 4 6666.67 6583 1.05 6695 0.12 5 1388.89 1473 5.09 1453 2.96 6 238.10 254 1.06 248 0.41 7 34.72 41 1.14 28 1.30 8 4.96 6 0.22 6 0.22 p=0.80437 p=0.47609 Number of rngs required: 688963, p-value: 0.741 RESULTS OF CRAPS TEST for dh-ranFile-2015-10-01_20:31 No. of wins: Observed Expected 98293 98585.9 z-score=-1.310, pvalue=0.09513 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66945 66666.7 1.162 1.162 2 37511 37654.3 0.546 1.708 3 26919 26954.7 0.047 1.755 4 19202 19313.5 0.643 2.398 5 13924 13851.4 0.380 2.779 6 9932 9943.5 0.013 2.792 7 7087 7145.0 0.471 3.263 8 5131 5139.1 0.013 3.276 9 3668 3699.9 0.274 3.550 10 2724 2666.3 1.249 4.799 11 1961 1923.3 0.738 5.537 12 1313 1388.7 4.131 9.668 13 1026 1003.7 0.495 10.162 14 741 726.1 0.304 10.467 15 532 525.8 0.072 10.539 16 365 381.2 0.684 11.223 17 276 276.5 0.001 11.224 18 208 200.8 0.256 11.480 19 147 146.0 0.007 11.487 20 117 106.2 1.095 12.582 21 271 287.1 0.904 13.487 Chisq= 13.49 for 20 degrees of freedom, p= 0.14446 SUMMARY of craptest p-value for no. of wins: 0.095126 p-value for throws/game: 0.144459 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2015-10-01_20:31 No. of wins: Observed Expected 98598 98585.9 z-score= 0.054, pvalue=0.52165 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66835 66666.7 0.425 0.425 2 37693 37654.3 0.040 0.465 3 27011 26954.7 0.117 0.582 4 19262 19313.5 0.137 0.719 5 13775 13851.4 0.422 1.141 6 9936 9943.5 0.006 1.147 7 7082 7145.0 0.556 1.703 8 5105 5139.1 0.226 1.929 9 3700 3699.9 0.000 1.929 10 2606 2666.3 1.364 3.292 11 1935 1923.3 0.071 3.363 12 1325 1388.7 2.926 6.289 13 989 1003.7 0.216 6.504 14 732 726.1 0.047 6.552 15 584 525.8 6.434 12.985 16 376 381.2 0.070 13.055 17 308 276.5 3.579 16.634 18 205 200.8 0.087 16.721 19 137 146.0 0.553 17.273 20 108 106.2 0.030 17.303 21 296 287.1 0.275 17.578 Chisq= 17.58 for 20 degrees of freedom, p= 0.38484 SUMMARY of craptest p-value for no. of wins: 0.521653 p-value for throws/game: 0.384845 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0000,0.0080,0.0114,0.0119,0.0137,0.0151,0.0152,0.0216,0.0243,0.0256, 0.0256,0.0257,0.0295,0.0358,0.0388,0.0401,0.0409,0.0416,0.0447,0.0569, 0.0603,0.0634,0.0700,0.0719,0.0751,0.0759,0.0785,0.0785,0.0880,0.0881, 0.0909,0.0951,0.1066,0.1129,0.1226,0.1299,0.1340,0.1341,0.1353,0.1416, 0.1445,0.1464,0.1483,0.1509,0.1519,0.1584,0.1591,0.1592,0.1607,0.1642, 0.1650,0.1803,0.1822,0.1825,0.1869,0.1992,0.2000,0.2076,0.2086,0.2094, 0.2145,0.2169,0.2180,0.2195,0.2233,0.2245,0.2319,0.2454,0.2492,0.2513, 0.2518,0.2525,0.2664,0.2713,0.2729,0.2762,0.2763,0.2782,0.2812,0.2883, 0.2922,0.2950,0.2961,0.2969,0.2995,0.3021,0.3034,0.3069,0.3119,0.3146, 0.3320,0.3327,0.3429,0.3515,0.3548,0.3625,0.3626,0.3743,0.3753,0.3789, 0.3848,0.3959,0.3992,0.4052,0.4216,0.4243,0.4271,0.4314,0.4316,0.4340, 0.4480,0.4569,0.4622,0.4671,0.4683,0.4685,0.4693,0.4702,0.4741,0.4752, 0.4761,0.4815,0.4855,0.4880,0.4926,0.4944,0.4952,0.4954,0.5043,0.5072, 0.5096,0.5099,0.5117,0.5198,0.5213,0.5217,0.5302,0.5325,0.5362,0.5364, 0.5423,0.5468,0.5559,0.5569,0.5611,0.5653,0.5701,0.5711,0.5735,0.5739, 0.5833,0.5921,0.5959,0.5967,0.6002,0.6038,0.6043,0.6060,0.6129,0.6139, 0.6156,0.6168,0.6234,0.6249,0.6253,0.6267,0.6269,0.6314,0.6329,0.6335, 0.6424,0.6480,0.6576,0.6594,0.6713,0.6715,0.6780,0.6813,0.6881,0.6898, 0.7160,0.7161,0.7174,0.7217,0.7220,0.7232,0.7235,0.7249,0.7299,0.7324, 0.7337,0.7343,0.7365,0.7396,0.7409,0.7435,0.7446,0.7575,0.7577,0.7593, 0.7603,0.7659,0.7756,0.7812,0.7850,0.7860,0.7878,0.7963,0.7983,0.8044, 0.8072,0.8084,0.8150,0.8164,0.8194,0.8300,0.8309,0.8347,0.8366,0.8467, 0.8532,0.8532,0.8607,0.8611,0.8648,0.8696,0.8710,0.8710,0.8750,0.8771, 0.8772,0.8775,0.8814,0.8867,0.8900,0.8928,0.8938,0.8968,0.9008,0.9010, 0.9046,0.9105,0.9215,0.9457,0.9485,0.9572,0.9586,0.9609,0.9617,0.9630, 0.9649,0.9667,0.9668,0.9683,0.9718,0.9741,0.9770,0.9787,0.9818,0.9831, 0.9836,0.9840,0.9858,0.9871,0.9917,0.9944,0.9961,0.9961,0.9984, Overall p-value after applying KStest on 269 p-values = 0.286133 In response to requests, we have provided a list of all the p-values produced by the tests you have chosen for this run. The individual p-values are supposed to be uniform in [0,1), but they are not necessarily independent. So even though we have applied a KSTEST to the accumulated p-values, the result is not necessarily---even if your file contains truly random bits---uniform in [0,1). But it is probably pretty close, so take that last p-value with a grain of salt. In particular, there may be some values so close to 0 or 1 that the tests they came from should be applied several more times, or new, related tests should be undertaken.